There is still dispute over the stability of endohedral metallofullerenes (EMFs) M2C2n, and recently, multiform lutetium-based dimetallofullerenes have been dropped in experiments. The thermodynamic stabilities of Lu2C86 EMFs are revealed by density functional theory (DFT) in conjunction with statistical thermodynamic analyses. Inevitably, besides the experimentally reported Lu-2@C-2v(63751)-C-86, Lu-2@C-s(63750)-C-86, and Lu-2@C-s(63757)-C-86, other three metal carbide clusterfullerenes, Lu2C2@D-2d(51591)-C-84, Lu2C2@C-1(51383)-C-84, and Lu2C2@C-s(id207430)-C-84, rather than Lu-2@C-86 are first characterized as thermodynamically stable isomers of Lu2C86. Specially, the C-s(id207430)-C-84 is a newly non-classical fullerene containing one heptagon, which is stabilized via encaging Lu2C2. Another interesting phenomenon is that the outer fullerene cages of thermodynamically stable Lu2C82-88 molecules are geometrically connected through C-2 addition/loss and Stone-Wales (SW) transformation, suggesting a special relationship between thermodynamic stabilities and geometries of Lu2C82-88 EMFs. Furthermore, the electronic configurations of (Lu-2)(4+)gC(86)(4-) and (Lu2C2)(4+)gC(84)(4-) were confirmed. A significantly stable two-center two-electron (2c-2e) Lu-Lu sigma single bond is formed in Lu-2@C-86. By comparing M-M bonds in M-2@C-2v(63751)-C-86 (M = Sc, Y, La, and Lu), two significant factors, the valence atomic orbital (ns) of metal atoms and radius of M2+, are found to determine the stability of the M-M bond in the C-2v(63751)-C-86. Additionally, the simulated UV-vis-NIR spectra of thermodynamically stable Lu2C86 isomers were simulated, which further disclose their electronic features.